The core concepts in mobius-land are local curvature and global cumulative field.

Then you accidentally make something truly 3D by intersecting things and realize you have no idea what you're looking at, couldn't imagine it if you closed your eyes, couldn't replicate it if you had a picture of the result and didn't know the 2D inputs that made it... and then you realize there are probably people out there who can see that entire design in their head.

To me it's like unicycling on a tightrope or skateboarding or realistic oil painting or playing piano well. I have no real concept or reference point for what that experience must be like.

I can't figure out any kind of way someone could do that with anything resembling what I understand "thought" to be like, so I assume you must be able to process entire sequences and their alternate possibilities simultaneously?

If true 3d printing* ever gets cheap, it'll be interesting to see how much form will be able follow function, rather than manufacturing cost.

* true 3d, as in overhang are allowed. Something like a cheap FDM is more 2.5d, since overhangs aren't allowed.

They're not quite unconstrained, and the layer adhesion strength makes some geometries not strong, but they're much more than 2.5D.

I think for me, the prerequisites for mastering CAD were 1) the practice I got visualizing 3D shapes so I could translate them into unambiguous mechanical drawings on paper (I swear, I'm not that old but my college was behind and we were the last class to actually do mechanical drawings with a pencil), and 2) having a procedural thought process from coding so that I could sequence the CAD operations to get where I want.

It's a block language where you program the object rather than manipulate shapes. It works well for my brain. Ymmv

I'm not a mechanical engineer, I mostly only do incidental CAD and hobby level work, so it's not really essential to have the deep understanding of space that real MEs need.

I often don't know what sequence of operations I'll need until I actually open the app. Generally it's more of an "Oh I need a mounting hole, lets look around on the screen and see where one could go" thing, a lot of the thinking is in the app rather than in the mind.

Of course you can't make nicely parametric things without a lot more thought so I will often wind up having to redo things that aren't one offs...

https://www.microwavejournal.com/articles/21001-printed-reso...

I have no idea if there are any advantages over a simple planar circular loop though.

2. Alternating currents will dissipate even with zero resistance, because the circuit will emit EM waves.

Those crazy electromagnets they use on these stellarator are simple superconducting loops that they 'charge' by inducing a current. That current is maintained so long as the superconductor stays below a certain temp. There is even something called a SMES (superconducting magnetic energy storage) that stores power this way, as I understand it they have a 0% self discharge rate.

If you have a hypothetical continuum of charges moving in a circle, and you use Maxwell’s equations, you’ll find that given a constant charge density, no EM radiation will be emitted.

If you have a superconductor, you should really be using quantum mechanics to understand it. If you can imagine that an electron can “orbit” a nucleus without emitting EM radiation, then you can imagine that current can flow in a loop without emitting EM radiation. The behavior cannot be explained by thinking of the behavior of a single electron, but must be explained by considering the behavior of many electrons in a quantum mechanical system.

Also note that the actual speed of electrons (the “drift velocity”) moving around a loop of wire is extremely low, so if you treat electrons as point charges and ignore quantum mechanics, and you calculate the amount of EM radiation that should be emitted by a typical loop of wire, you will get an extremely low amount EM radiation emitted, which would be very difficult to measure.

I spent a lot time staring at Escher images as a teen, so I think my brain says "yes please". I have no idea what to do with any of it, so it's not like it does me any good.